Home > mpt > @polytope > size.m

# size

## PURPOSE

SIZE Returns size of the given polytope object

## SYNOPSIS

function [nx,ny] = size(P,a)

## DESCRIPTION

```SIZE Returns size of the given polytope object

[nx,ny]=size(P,a)

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DESCRIPTION
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[NX,NY] = SIZE(P)

If P is a single polytope, NX and NY will be both 1

If P is an array of polytopes, NY contains number of element in the
array. NX will be always 1.

NOTE: In order to access number of constraints and dimension of P,
please use NCONSTR and DIMENSION respectively.

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INPUT
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P      - polytope (or a polytope array)
a      - index

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OUTPUT
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nx     - is 1 always
ny     - number of elements in P (i.e. length(P))

## CROSS-REFERENCE INFORMATION

This function calls:
• length LENGTH Returns number of regions over which the explicit control law is defined
• end END Returns the last element in a given polytope array
• length LENGTH Returns number of elements in a polytope array
This function is called by:
• info INFO Displays more detailed information a given MPT controller
• mptctrl MPTCTRL Constructor for the MPT controller object
• addMLDconstraints ADDMLDCONSTRAINTS Adds state and output constraints to MLD matrices
• sim SIM Simulates a given controller
• simplot SIMPLOT Plots a simulated trajectory
• and AND Intersection of n polytopes
• bounding_box BOUNDING_BOX Compute a bounding box for a given polytope
• chebyball CHEBYBALL Computes center and radius of the largest ball inscribed in a polytope
• dimension DIMENSION Returns dimension of the given polytope
• display DISPLAY Displays details about the given polytope
• distance DISTANCE Distance between two sets
• distribpoints DISTRIBPOINTS Distribute n points such that distances between them are maximized
• domain DOMAIN Computes polytope that is mapped to an another polytope using affine map
• envelope ENVELOPE Computes envelope of n polytopes
• eq EQ Checks if two polytopes are equal
• extreme EXTREME Calculates extreme points of a given polytope
• facetcircle FACETCIRCLE Returns largest circle inside facet 'ind' of polytope P
• facetvoronoi FACETVORONOI Computes an equivalent of voronoi diagrams for facets
• getInnerEllipsoid GETINNERELLIPSOID Computes the largest ellipsoid inscribed in a polytope
• getOutterEllipsoid GETOUTTERELLIPSOID Computes the smallest ellipsoid which covers the polytope P
• horzcat HORZCAT Concatenates polytopes into a polytope array
• isbounded ISBOUNDED Checks if a polytope is bounded
• isinside ISINSIDE Checks if a given point lies in the interior of a given polytope
• isredundant ISREDUNDANT Check if a constraint is redundant
• le LE Checks if polytope P is a subset of polytope Q
• lt LT Checks if polytope P is a strict subset of polytope Q
• minus MINUS Pontryagin difference
• mtimes MTIMES Polytope multiplication
• nconstr NCONSTR Returns number of constraints that form an H-representation of a polytope
• normalize NORMALIZE Normalizes a given polytope
• plot PLOT Plots polytopes in 2D or 3D
• plus PLUS Minkowski sum of two polytopes
• polytope POLYTOPE Default constructor for the POLYTOPE object
• chebyball_f CHEBYBALL_F Computes center and radius of the largest ball inscribed in a polytope
• lrsextreme
• projection PROJECTION Projection of a polytope or a polytope array
• range RANGE Affine transformation of a polytope
• reduce REDUCE Reduces the polytope by removing redundant inequalities
• regiondiff REGIONDIFF Region difference
• regiondiffXU REGIONDIFFXU Computes region difference in lifted XU space
• triangulate TRIANGULATE Calculates triangulation of arbitrary polytopes
• union UNION convex union computation
• unique UNIQUE Removes redundant entries from a polytope array
• vertcat VERTCAT Concatenates polytopes into a polytope array
• volume VOLUME Calculates volume of a polytope
• ballandplatedemo "Ball and Plate" demo
• pwa4d PWA3D 3rd order PWA example with 2 PWA dynamics
• ownmpc7
• mpt_checkLyapFct MPT_CHECKLYAPFCT Checks if a function is a Lyapunov function for a given ctrlStruct
• mpt_computePWATset MPT_COMPUTEPWATSET Computes a stabilizing control invariant set (+ controllers) around the origin
• mpt_dlyap_infnorm Lyapunov equation with inf-norm for discrete-time LTI systems
• mpt_getCommonSOSLyapFct MPT_GETCOMMONSOSLYAPFCT Calculates Common SOS Lyapunov function for system with additive disturbance
• mpt_getPWALyapFct MPT_GETPWALYAPFCT Calculates PWA Lyapunov function
• mpt_getPWPLyapFct MPT_GETPWPLYAPFCT Calculates Piecewise Polynomial (sum of squares) Lyapunov function
• mpt_getPWQLyapFct MPT_GETPWQLYAPFCT Calculates PWQ Lyapunov function
• mpt_getQuadLyapFct MPT_GETQUADLYAPFCT Computes common Lyapunov function for PWA system
• mpt_getReachSubset MPT_GETREACHSUBSET Computes a subset of P which enters Pfin
• mpt_infset MPT_INFSET Calculates the maximal positively invariant set for an LTI system
• mpt_infsetPWA MPT_INFSETPWA Computes (robust) positive invariant subset for PWA systems
• mpt_isPWAbigger MPT_ISPWABIGGER Test if one PWA function is bigger than a second PWA function
• mpt_maxCtrlSet MPT_MAXCTRLSET Computes the maximal robust control invariant set C_inf
• mpt_reachSets MPT_REACHSETS Computes sets of reachable states for a given system / controller
• mpt_reachXU MPT_REACHXU One-step reachability computation for an affine system
• mpt_removeOverlaps MPT_REMOVEOVERLAPS Removes overlaps from (a set of) polyhedral partitions with associated linear cost
• mpt_searchTree MPT_SEARCHTREE Computes a search-tree for a given explicit solution
• mpt_transmap MPT_TRANSMAP Computes transition map
• mpt_verify MPT_VERIFY Verifies if states enter a given set in a given number of steps
• mpt_evalPWA MPT_EVALPWA Evaluates a PWA function at a given location
• mpt_feasibleStates MPT_FEASIBLESTATES returns equidistantly spaced data points in feasible set
• mpt_getCommonLyapFct MPT_GETCOMMONLYAPFCT Computes common Lyapunov function for PWA system
• mpt_getFullRankSubset MPT_GETFULLRANKSUBSET Removes rows from matrix Gt until it has full row rank
• mpt_ineq2eq MPT_INEQ2EQ Detects inequality constraints whihc form equalities
• mpt_lrs MPT_LRS Matlab implementation of the LRS algorithm
• mpt_lti2pwa MPT_LTI2PWA Converts an LTI system to a PWA system
• mpt_mplp_ver1 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver2 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver3 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver4 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver5 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver6 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver7 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_norm2pwa MPT_NORM2PWA transformes a linear norm into an equivalent PWA fcn representation
• mpt_optControlPWAold MPT_OPTCONTROLPWA Solves the CFTOC problem for a given PWA system
• mpt_performance MPT_PERFORMANCE Computes performance (i.e. sum of closed-loop costs) associated to a given controller
• mpt_prepareDU MPT_PREPAREDU Extends system and problem matrices to deal with deltaU constraints
• mpt_prepareTracking MPT_PREPARETRACKING Extends system and problem matrices to deal with tracking
• mpt_pwa2hys MPT_PWA2HYS Converts a PWA system described in sysStruct into a HYSDEL model
• mpt_solveLPi MPT_SOLVELPi Interface to various LP solvers (version without errorchecks)
• mpt_sysStructInfo MPT_SYSSTRUCTINFO Returns information about system structure
• mpt_verifyProbStruct MPT_VERIFYPROBSTRUCT Verifies the probStruct structure
• mpt_verifySysProb MPT_VERIFYSYSPROB Verifies system and problem structures
• mpt_verifySysStruct MPT_VERIFYSYSSTRUCT Verifies the sysStruct structure
• mpt_yalmipDU MPT_YALMIPDU Augmentes the system to cope with deltaU constraints
• mpt_yalmipTracking MPT_YALMIPTRACKING Extends system and problem matrices to deal with tracking
• sub_computeTrajectory sub_COMPUTETRAJECTORY Calculates time evolution of state trajectories subject to control
• sub_getyalmipdata SUB_GETYALMIPDATA Internal function
• sub_setyalmipdata Copyright is with the following author(s)
• PWAwelldefined 1.) check if the polyhedral partition covers the whole xr-ur space defined
• hys2pwa HYS2PWA Transformation of HYSDEL model into PWA model
• mpt_hyparr ===============================================================================
• mpt_pwa2mld MPT_PWA2MLD Converts a PWA system into the MLD representation
• mpt_pwa2sys MPT_PWA2SYS Converts structure generated by hys2pwa.m to a sysStruct structure
• remAL ===============================================================================
• syminfo info = syminfo(S, vname, vtype, vkind, vindex)
• gen_log ===============================================================================
• mpc_buildmatFAST ===============================================================================
• mpc_checkSysWeight ===============================================================================
• mpc_mip ===============================================================================
• mpt_blockingMatrices MPT_BLOCKINGMATRICES Constructs matrices for the CFTOC problem for move blocking strategies
• mpt_boolMinTime MPT_BOOLMINTIME Computes minimum time controller for systems with discrete inputs
• mpt_constructMatrices MPT_CONSTRUCTMATRICES Constructs matrices for the finite time constrained optimal control problem
• mpt_getInputXU MPT_GETINPUTXU For a given state, extracts the an output from an XUset
• mpt_getStabFeedback MPT_GETSTABFEEDBACK Computes a stabilizing feedback law for a PWA system
• mpt_iterative MPT_ITERATIVE Computes a time-optimal or low-complexity explicit controller for LTI systems
• mpt_iterativePWA MPT_ITERATIVEPWA Computes a time-optimal or low-complexity explicit controller for PWA systems
• mpt_mixedMinTime MPT_MIXEDMINTIME Computes minimum time controller for systems with discrete and continuous inputs
• mpt_optBoolCtrl MPT_OPTBOOLCTRL Computes optimal controller for systems with discrete inputs
• mpt_optControl MPT_OPTCONTROL Solves the CFTOC problem for a given LTI system
• mpt_optControlPWA MPT_OPTCONTROLPWA Solves the CFTOC problem for a given PWA system
• mpt_optInfControl MPT_OPTINFCONTROL Solves the infinite-time constrained optimal control problem for LTI systems
• mpt_optInfControlPWA MPT_OPTINFCONTROLPWA Solves the infinite-time constrained optimal control problem for PWA systems
• mpt_optMixedCtrl MPT_OPTMIXEDCTRL Computes optimal controller for systems discrete and continuous inputs
• mpt_optQuadCtrl MPT_OPTQUADCTRL CFTOC of PWA systems with quadratic cost
• mpt_simplexContr MPT_SIMPLEXCONTR Computes a piecewise affine feedback law defined over simplices
• mpt_solveMPC MPT_SOLVEMPC Solves the on line optimization MPC problem
• mpt_yalmipcftoc MPT_YALMIPCFTOC CFTOC of PWA systems
• mpt_hyparr2 ===============================================================================
• mpt_merge5 ===============================================================================
• mpt_optMerge ===============================================================================
• mpt_optMergeDivCon ===============================================================================
• polyinnerball CHEBYBALL_F Computes center and radius of the largest ball inscribed in a polytope
• tg_polyreduce
• writeEspressoOnOff ===============================================================================
• hull HULL Converts vertices/polytope array into an H-representation polytope
• mpt_delaunay MPT_DELAUNAY Computes the delaunay triangulation of a polytope
• mpt_voronoi MPT_VORONOI Computes the voronoi diagram via mpLP
• mpt_getInnerEllipsoid MPT_GETINNERELLIPSOID Computes the largest ellipsoid inscribed in a polytope
• mpt_getOutterEllipsoid MPT_GETOUTTERELLIPSOID Computes the smallest ellipsoid which covers the polytope P
• mpt_plotArrangement MPT_PLOTARRANGEMENT Plots hyperplane arrangement of a polytope in H-representation
• mpt_plotPWA MPT_PLOTPWA Plots a PWA function defined over a given polyhedral partition
• mpt_plotPWQ MPT_PLOTPWQ Plots a PWQ function defined over polyhedral partition
• mpt_plotPartition MPT_PLOTPARTITION Plots a polyhedral partition obtained by mpt_control
• mpt_plotSysStruct MPT_PLOTSYSSTRUCT Plots the system partitions of a PWA system
• mpt_plotTimeTrajectory MPT_PLOTTIMETRAJECTORY Plots trajectories of states, inputs, outputs and disturbances
• mpt_plotTrajectory MPT_PLOTTRAJECTORY Graphical interface for piloting trajectories for LTI and PWA systems subject to control
• mpt_plotU MPT_PLOTU For a given explicit controller, plots value of the control action
• mpt_computeTrajectory MPT_COMPUTETRAJECTORY Calculates time evolution of state trajectories subject to control
• mpt_control MPT_CONTROL Main control routine. Computes explicit controller for a given problem
• mpt_getInput MPT_GETINPUT For a given state, extracts the (optimal) output from a controller structure
• mpt_init MPT_INIT Initializes the MPT toolbox
• mpt_invariantSet MPT_INVARIANTSET Computes (robust) positive invariant subset of an explicit controller
• mpt_simSys MPT_SIMSYS Simulates evolution of a given system
• mpt_simplify MPT_SIMPLIFY simplifies a given explicit controller by merging regions with identical control law
• mpt_mpmilp MPT_MPMILP Multi-Parametric Mixed-Integer LP solver
• mpt_mpmiqp MPT_MPMIQP Multi-Parametric Mixed-Integer QP solver
• mpt_mpqp MPT_MPQP Explicitly solves the given quadratic program (QP)
• mpt_solveLP MPT_SOLVELP Interface to various LP solvers
• mpt_solveMILP MPT_SOLVEMILP Interface to various MILP solvers
• mpt_solveMIQP MPT_SOLVEMIQP Interface to various MIQP solvers
• mpt_solveQP MPT_SOLVEQP Interface to various QP solvers

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